Question

Suppose chang places $7000 and an account that pays 2% interest compounded each year. Assume that no withdraws are made from the account.Follow the instructions below. Do not do any rounding

Answer 1

In general, the compound interest formula is

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ P\rightarrow\text{ initial amount} \\ r\rightarrow\text{ interest rate} \\ n\rightarrow\text{ number of times the interest is applied per period of time \lparen t\rparen} \\ t\rightarrow\text{ years} \end{gathered}`

In our case, since it is not specified how often the interest is compounded, we will assume that n=1; then,

`A=7000(1+(0.02)/(1))^(1*t)=7000(1.02)^t`

a) Set t=1

`\begin{gathered} t=1 \\ \Rightarrow A(1)=7000(1.02)^t=7140 \\ \end{gathered}`

The answer to part a) is 7140

b) Set t=2,

`A(2)=7000(1.02)^2=7282.8`

The answer to part b) is 7282.8

Notice that we are not given the number of times the interest is applied per year; therefore, we had to assume that it compounds 1 time annually.